Distribution Free Tests of Independence Based on the Sample Distribution Function

1961/06/01 by J. R. Blum, J. Kiefer, M. Rosenblatt · 498 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Applied mathematics #Asymptotic distribution #Bayesian Methods and Mixture Models #Bivariate analysis #Distribution (mathematics) #Distribution function #Estimator #Independence (probability theory) #Mathematical analysis #Mathematics #Power function #Sample (material) #Statistical Distribution Estimation and Applications #Statistics

paper · pdf · doi:10.1214/aoms/1177705055

published in The Annals of Mathematical Statistics 32(2), 485-498 (Institute of Mathematical Statistics)

openalex publication_date 1961/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Certain tests of independence based on the sample distribution function (d.f.) possess power properties superior to those of other tests of independence previously discussed in the literature. The characteristic functions of the limiting d.f.'s of a class of such test criteria are obtained, and the corresponding d.f. is tabled in the bivariate case, where the test is equivalent to one originally proposed by Hoeffding [4]. A discussion is included of the computational problems which arise in the inversion of characteristic functions of this type. Techniques for computing the statistics and for approximating the tail probabilities are considered.

Citations

• Application of the Method of Mixtures to Quadratic Forms in Normal Variates
• Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes
• A Non-Parametric Test of Independence

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